Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces

Brendan Hassett, Sho Tanimoto, Yuri Tschinkel

Research output: Contribution to journalArticle

Abstract

Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanced line bundles, and prove the required inequalities for a large class of equivariant compactifications of homogeneous spaces.

Original languageEnglish (US)
Pages (from-to)6375-6410
Number of pages36
JournalInternational Mathematics Research Notices
Volume2015
Issue number15
DOIs
StatePublished - 2015

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Geometric Invariants
Line Bundle
Homogeneous Space
Compactification
Equivariant
Rational Points
Projective Variety
Asymptotic Formula
Imply
Predict
Class
Framework
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces. / Hassett, Brendan; Tanimoto, Sho; Tschinkel, Yuri.

In: International Mathematics Research Notices, Vol. 2015, No. 15, 2015, p. 6375-6410.

Research output: Contribution to journalArticle

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